Dissension is growing among some members of the Washington Teachers' Union as criticism of alleged mismanagememt by the union's officials, particularly union president William Simons, circulates among union members.

The dissension comes as the union's officials announced yesterday that unless "real progress" is made in negotiations with the D.C. school board today they will call a strike beginning at 12:01 a.m. tomorrow.

"Setting the Tuesday strike date is not a threat to the negotiators," Simons told the Associated Press, "but simply letting the [school] board know that teachers, who have aoted with the patience of Job, will not be led down the path of slavery."

The union's strike preparations in the last two weeks have not quieted the dissension within the union. They have served, instead, to focus attention on the union's leaders and the way the union is managed. A central question being asked by union members is why, after promises made during a two-week strike in 1972, the union still does not have a strike fund.

Interviews with dozens of teachers show that questions are being asked about other issues as well:

The alleged inability of the union to help the majority of teachers who file grievances against the school system. According to teachers, union officials say they are swamped with grievances and have to decide which cases deserve the most immediate attention.

The union's retirement fund for persons on the union staff and the use of a general expenses fund by union officials.

The recent vote by the union's executive committee, including Simons and union vice president Lynnwood Williamson, to create another paid position on the union staff. Williamson immediately resigned his nonpaying position with the union to take the post.

Most troubling of all for union president Simons is the fact that teachers, for the first time, are beginning to discuss openly whether he has been president of the union for too long.He has been president since 1964.

More militant members of the union accuse Simons of "shuffling and jiving' when he said he would stop negotiating and call a strike if the school board did not extend the teachers' old contract past Feb. 14. The board did not extend the contract. The union remained at the bargaining table and only yesterday called for a strike.

The dissension is by no means indicative of the attitudes of most umion members toward Simons. To most of the members, he remains unquestionably their leader and spokesman.

Simons would not answer any questions about the union when a reporter tried to interview him on two occasions. He grew angry when he learned that union members and the union's auditors were being questioned.

The dissension among union members surfaced recently when Simons, at a closed meeting held last week to discuss preparations for a strike, leaned over the podium and stared intently into the faces of union representatives from every school in the city.

"Ihve heard that some teachers in some schools are taking votes to decide whether teachers at that particular school are going to go out," Simons said. "The vote has already been taken. We have strike authorization. This is no time for backstepping."

The dissension was apparent at the union meeting last Monday night when the union's membership voted to give Simons and the union's executive committee authority to call a strike. After firing up the teachers with a speech calling for "respect and dignity" for teachers at any price, as well as the resignation of the "incompetent" D.C. school board, Simons began speaking quickly and asked for any questions or discussion. Seconds later, before any response could be made, Simons called for a vote.

The union membership resounded with "ayes" but later, as the teachers filed out, the church resounded with widespread grumbling.

"What you just saw was Bill Simons' peprally," said Jim Ricks, a teacher at Ballou High School. "Every two years, when it is time for the union to elect a new president, some kind of crisis comes up so teachers are battling with the school system and don't have time to talk about what's going on inside the union... The contract expired in January '78. All this could have been done last year but Simons waited until now, right before he is up for election in May."

The predominant area of union activities being questioned by the teachers is the union's use of the approximately $700,000 per year it collects in dues.

"The union takes in near to $60,000 a month," said Arthur Haynes, a teacher at Fletcher-Johnson Junior High, "and no one but Bill Simons knows what happens to it. The union books don't balance. No one knows how much Simons is paid or how much it costs for them to have offices in that expensive building downtown."

Despite the allegations and questions, Simons remains the personification of the Washington Teachers' Union.

"You have dissenters in the church of God," said Sarah Banks, a teacher at Deal Junior High. "So you are going to have dissenters in Bill Simons' union. Most of the dissenters do it behind his back but they don't have the guts to do it in front of his face."

After a recent union meeting at the Metropolitan AME Church Simons stood beneath the arched doorway to the church's M Street entrance like a country preacher tending to his flock after Sunday services.

As the public school teachers -- most of whom were middle-aged women who teach elementary school -- went out, they would stop to hug or kiss Simons. The men, their hats in their hands, would stop to shake hands and say a few words.

"Are we going to have a strike?" a woman with graying hair asked Simons. "I've seen you on TV and you know we'll do whatever you say, Mr. Simons. You're my union."

For that teacher and for teachers throughout the city, fans and detractors alike, Simons is the Washington Teachers' Union. Simons' face -- his mouth stretched wide with a grin -- is the face of the union, its symbol. His voice -- a slow, measured way of talking, often broken by nervous giggling -- remains the voice of the union, and his decisions remain the union's decisions.

Many teachers openly admit to not understanding what issues separate the union and the board at the bargaining table -- other than board proposals to give teachers a longer school year and school day -- but the teachers generally say they have unending faith in whatever Simons decides to do.

The issues between the union and the board are similar to the issues that Simons said he wanted to negotiate with the school system during his 1967 campaign to win the teachers' support for the Washington Teachers' Union as their collective bargaining agent.

"I think this vote is clearly a mandate for change," Simons said in 1967 after his union won the right to represent teachers. 'It is a protest against the way the public school system in Washington is now being operated."

In September 1967 Simons appeared before the school board and told them that the union was determmined to "take part in educational policy decisions," and change the school system's procedure for handling the grievances of teachers.

Many of those same issues are at the heart of the disagreement between the board and the union today. The board, under much pressure from parents and political figures to improve the school system, has said that past boards gave the union too much say in the policies of the school system and the quality of education in city schools has suffered for it.

Board members have said they intend to regain in the current negotiations many of the concessions made to the union by past boards.